Arrays of first-order steerable differential microphones

The literature is rich with techniques for the design of small-size Differential Microphone Arrays (DMAs), known for their almost frequency-invariant beampatterns and low computational cost. Few works, instead, discuss the properties of beamformers based on multiple DMA units. In this paper, we consider arbitrarily shaped planar arrays of DMA units. In turn, each DMA unit is a first-order continuously-steerable differential microphone characterized by an arbitrary configuration of omnidirectional sensors and a symmetric beampattern. We present a beamforming technique that, assumed all the DMA units to steer identical beams in the same direction, allows us to approach the behavior of a Delay-And-Sum beamformer or Super-Directive beamformer by solely varying a single scalar parameter. Efficient implementations of the proposed beamformers can be developed by taking into account that, for a wide range of frequencies, the values of such a parameter are practically invariant with respect to the geometry of the array.